6 replies to this topic

[Contextions]

There is a cylinder on it's side - positioned like a tanker truck - with only only the height of the fluid inside being known. How do you determine the filled volume? I have seen a table in which you look up the height and it tells you the volume percentage but I can not find it anywhere. I also used to know how to differentiate the volume based on a changing variable - the height - but can not remember anymore. Can someone please help me out?

[JoeWong]

Contextions,

Welcome !

Please make full use of SEARCH function in this forum...

Mr. Montemayor has prepared a fantastic excel sheet to calculate the liquid filled volume in vessel.
Please download from this link...

• VESSEL VOLUME

[bmk]

 C.S.H.CYL..bmp   960.05KB   115 downloads  C.S.H.CYL..bmp   960.05KB   115 downloads[attachment=1058
:C.S.H.CYL..bmp]  C.S.H.CYL..bmp   960.05KB   115 downloads

There is a cylinder on it's side - positioned like a tanker truck - with only only the height of the fluid inside being known. How do you determine the filled volume? I have seen a table in which you look up the height and it tells you the volume percentage but I can not find it anywhere. I also used to know how to differentiate the volume based on a changing variable - the height - but can not remember anymore. Can someone please help me out?

To

Contextions

I am a chemical engineer from University of Bombay(Mumbai) with M.chem.Engg. degree to my credit. The problem faced by you is very common but not well attended. I am attaching here a chart for your kind reference. You can verify with atual tank dimensions.---- B.M.Khare
CHART FOR VOLUME /DEPTH IN HORIZONTAL CYLIDER
The adjacent figure is cross section of a horizontal cylinder. The volume of any liquid in the section AMBN= AreaAMBN*length of cylinder. AreaAMBN varies proportionately with depth MN and so the volume of liquid in the horizontal cylinder is not linearly proportional to the depth as in the vertical cylinder. Therfore to make a chart of Vol./depth actually implies calculation of areaANBM for all values of MN in the range (0, ON) upto half the depth.

Let ON=radius R ,depth MN= h, OM=R-h,
AngleAOB= O radians
Area ANBM= Area sector OANB - Area of triangle OAB
= 0.5*O*R^2 -0.5R^2sin O
=0.5*R^2 ( O -sinO)
Area ANBM/total c.s.area =
(0.5/3.142)( O -sinO)
=0.1591)( O -sinO)------------1 Volume fraction v
h is related to angle O as follows:-
h= R-Rcos O/2
h/R = 1-cos O/2----------2 Depth fraction d
We will use above relations to make a chart for volume fraction /depth fraction in the lower half of the cylinder.



























No. h/R cos O/2 angleO/2 angle O sinO v
1 0.0500 0.9500 0.3176 0.6351 0.5933 0.0067
2 0.1000 0.9000 0.4510 0.9021 0.7846 0.0187
3 0.1500 0.8500 0.5548 1.1096 0.8955 0.0341
4 0.2000 0.8000 0.6435 1.2870 0.9600 0.0520
5 0.2500 0.7500 0.7227 1.4455 0.9922 0.0721
6 0.3000 0.7000 0.7954 1.5908 0.9998 0.0940
7 0.3500 0.6500 0.8632 1.7264 0.9879 0.1175
8 0.4000 0.6000 0.9273 1.8546 0.9600 0.1423
9 0.4500 0.5500 0.9884 1.9769 0.9187 0.1684
10 0.5000 0.5000 1.0472 2.0944 0.8660 0.1954
11 0.5500 0.4500 1.1040 2.2081 0.8037 0.2234
12 0.6000 0.4000 1.1593 2.3186 0.7332 0.2522
13 0.6500 0.3500 1.2132 2.4265 0.6557 0.2817
14 0.7000 0.3000 1.2661 2.5322 0.5724 0.3118
15 0.7500 0.2500 1.3181 2.6362 0.4841 0.3424
16 0.8000 0.2000 1.3694 2.7389 0.3919 0.3734
17 0.8500 0.1500 1.4202 2.8405 0.2966 0.4047
18 0.9000 0.1000 1.4706 2.9413 0.1990 0.4363
19 0.9500 0.0500 1.5208 3.0416 0.0999 0.4680
20 1.0000 0.0000 1.5708 3.1416 0.0000 0.4998

[bmk]

for calculating volume fraction when tank is filled above its centerline refer the attached diagrm and chart.

No. h/R cos O/2 Angle O/2 Angle O sin O O/(2*3.1416) sinO/(2*3.1416) v
1 1.0500 0.0500 1.5208 3.0416 0.0999 0.4841 0.0004 0.5163
2 1.1000 0.1000 1.4706 2.9413 0.1990 0.4681 0.0007 0.5326
3 1.1500 0.1500 1.4202 2.8405 0.2966 0.4521 0.0010 0.5490
4 1.2000 0.2000 1.3694 2.7389 0.3919 0.4359 0.0014 0.5655
5 1.2500 0.2500 1.3181 2.6362 0.4841 0.4196 0.0017 0.5821
6 1.3000 0.3000 1.2661 2.5322 0.5724 0.4030 0.0020 0.5990
7 1.3500 0.3500 1.2132 2.4265 0.6557 0.3862 0.0023 0.6161
8 1.4000 0.4000 1.1593 2.3186 0.7332 0.3690 0.0026 0.6336
9 1.4500 0.4500 1.1040 2.2081 0.8037 0.3514 0.0028 0.6514
10 1.5000 0.5000 1.0472 2.0944 0.8660 0.3333 0.0031 0.6697
11 1.5500 0.5500 0.9884 1.9769 0.9187 0.3146 0.0032 0.6886
12 1.6000 0.6000 0.9273 1.8546 0.9600 0.2952 0.0034 0.7082
13 1.6500 0.6500 0.8632 1.7264 0.9879 0.2748 0.0035 0.7287
14 1.7000 0.7000 0.7954 1.5908 0.9998 0.2532 0.0035 0.7503
15 1.7500 0.7500 0.7227 1.4455 0.9922 0.2301 0.0035 0.7735
16 1.8000 0.8000 0.6435 1.2870 0.9600 0.2048 0.0034 0.7986
17 1.8500 0.8500 0.5548 1.1096 0.8955 0.1766 0.0032 0.8266
18 1.9000 0.9000 0.4510 0.9021 0.7846 0.1436 0.0028 0.8592
19 1.9500 0.9500 0.3176 0.6351 0.5933 0.1011 0.0021 0.9010
20 2.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000

[bmk]

Attached Files

•  C.S.H.CYL..2.bmp   1.26MB   60 downloads

[Markel]

How do I calculate a hortizontal vessel laying on it side but it has a slope. One end would be 11 in higher than the other end. The hortizontal vessel is 180 feet long. See uploaded picture for guide.

Thanks

Attached Files

•  vessel.bmp   2.64MB   54 downloads

[djack77494]

How do I calculate a hortizontal vessel laying on it side but it has a slope.

Markel,
Good question and one that would be fairly difficult to do based on first principles. I refer you to the internet site:

www.xcalcs.com

where you will find what you need. (I need to learn how to put a link into a reply.)